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A new modularity measure for Fuzzy Community detection problems based on overlap and grouping functions

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Gomez, D. and Rodríguez, Juan Tinguaro and Yáñez, Javier and Montero, Javier (2016) A new modularity measure for Fuzzy Community detection problems based on overlap and grouping functions. International Journal of Approximate Reasoning, 74 . pp. 88-107. ISSN 0888-613X

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Official URL: http://www.sciencedirect.com/science/article/pii/S0888613X16300305


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Abstract

One of the main challenges of fuzzy community detection problems is to be able to measure the quality of a fuzzy partition. In this paper, we present an alternative way of measuring the quality of a fuzzy community detection output based on n-dimensional grouping and overlap functions. Moreover, the proposed modularity measure generalizes the classical Girvan–Newman (GN) modularity for crisp community detection problems and also for crisp overlapping community detection problems. Therefore, it can be used to compare partitions of different nature (i.e. those composed of classical, overlapping and fuzzy communities). Particularly, as is usually done with the GN modularity, the proposed measure may be used to identify the optimal number of communities to be obtained by any network clustering algorithm in a given network. We illustrate this usage by adapting in this way a well-known algorithm for fuzzy community detection problems, extending it to also deal with overlapping community detection problems and produce a ranking of the overlapping nodes. Some computational experiments show the feasibility of the proposed approach to modularity measures through n-dimensional overlap and grouping functions.


Item Type:Article
Uncontrolled Keywords:Aggregation operators; Grouping functions; Overlap functions
Subjects:Sciences > Mathematics > Operations research
ID Code:37647
Deposited On:13 May 2016 10:15
Last Modified:02 Jun 2016 17:22

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